# Machine learning surrogates for efficient hydrologic modeling: Insights from stochastic simulations of managed aquifer recharge

arXiv: https://arxiv.org/abs/2407.20902 · HTML: https://mlsanity.com/paper/2407.20902/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Object Detectors Emerge in Deep Scene CNNs](https://mlsanity.com/paper/1412.6856/) (2014)
- [PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning](https://mlsanity.com/paper/1804.06300/) (2018)
- [Semantic Hierarchy Emerges in Deep Generative Representations for Scene Synthesis](https://mlsanity.com/paper/1911.09267/) (2019)

## Built on by (most cited first, 1 of 1)

- [HydroStartML: A combined machine learning and physics-based approach to reduce hydrological model spin-up time](https://mlsanity.com/paper/2504.17420/) (2025)

## Abstract (arXiv)

Process-based hydrologic models are invaluable tools for understanding the terrestrial water cycle and addressing modern water resources problems. However, many hydrologic models are computationally expensive and, depending on the resolution and scale, simulations can take on the order of hours to days to complete. While techniques such as uncertainty quantification and optimization have become valuable tools for supporting management decisions, these analyses typically require hundreds of model simulations, which are too computationally expensive to perform with a process-based hydrologic model. To address this gap, we assess a hybrid modeling workflow in which a process-based model is used to generate an initial set of simulations and a machine learning (ML) surrogate model is then trained to perform the remaining simulations required for downstream analysis. As a case study, we apply this workflow to simulations of variably saturated groundwater flow at a prospective managed aquifer recharge site. We compare the accuracy and computational efficiency of several ML architectures, including deep convolutional networks, recurrent neural networks, vision transformers, and networks with Fourier transforms. Our results demonstrate that ML surrogate models can achieve under 10% mean absolute percentage error and yield order-of-magnitude runtime savings over process-based models. Building on these findings, we examine the impacts of key modeling choices on surrogate model accuracy and efficiency. Results show that a normalized loss function improves training stability, while min-max data normalization can significantly reduce error up to a factor of 10 when compared to other treatments such as Z-score and no normalization. Downsampling input features using an autoencoder also decreases memory requirements by training with tensors 4% their original size. By reducing computational costs and...